==== Basic Properties of Light ====
**1. Overview**\\
Light is electromagnetic radiation exhibiting wave-particle duality, serving as a fundamental carrier for energy transfer and information transmission in modern technology.\\

Its behavior is described by three core models:\\
  * The **ray model** for macroscopic propagation paths;
  * The **wave model** for microscopic interference and diffraction;
  * The **photon model** for its quantized energy nature.
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**2.Ray Model**\\
The Ray Model is the most basic optical approximation, ignoring wave-particle duality effects.It describes light propagation as geometric rays along straight paths, grounded in Fermat’s Principle: light travels along paths of extremal optical path length (maximum, minimum, or stationary).Its behavior follows three fundamental laws:\\
**2.1 Law of Rectilinear Propagation**\\
In a homogeneous medium, light propagates in a straight line.\\
This law explains macroscopic phenomena (e.g., solar eclipses, pinhole imaging, shadow formation) and underpins all geometric optical systems.\\

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**2.2 Law of Reflection**\\
When incident on a medium interface, a light ray obeys two rules: 
  - The angle of incidence equals the angle of reflection:$\theta_i = \theta_r$
  - The incident ray, reflected ray, and surface normal lie in the same plane. 
{{ en:yanding:imaging_basics:optics:geometric_optics:光3.png?280 |}}
Both angles are measured relative to the surface normal.This law governs all specular reflection, as demonstrated by mirror imaging of a coin and landscape reflections in a calm lake .
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**2.3 Law of Refraction(Snell’s Law)**\\
When light crosses the interface between two media with different refractive indices ($n_1$ and $n_2$ ), its path bends according to:\\
$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$
where $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, measured from the surface normal. 
{{ :en:yanding:imaging_basics:optics:geometric_optics:光5.png?500 |}}
This law quantifies refraction and is the fundamental principle behind the operation of lenses, prisms, and other refractive optics. A classic demonstration is the apparent bending of a straight object, like a pencil, partially immersed in water.  
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**3.Wave Model**\\
This model describes light as an electromagnetic wave. The figure illustrates its typical transverse wave characteristics: electric and magnetic field vectors vary sinusoidally in a plane perpendicular to the direction of propagation. \\
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Its core wave properties are exhibited through phenomena such as interference (exemplified by double-slit interference fringes), diffraction (exemplified by single-slit diffraction), and polarization (exemplified by circular polarization).
{{ :en:yanding:imaging_basics:optics:geometric_optics:光8.png?800 |}}
The relationship between the speed of light, wavelength, and frequency is given by the fundamental equation:
$$c = \lambda \nu$$
where：\\
  * $c$: speed of light in vacuum,
  * $\lambda$ : wavelength of light,
  *$ \nu$ : frequency of light.
When $c$ is constant, a longer wavelength corresponds to a lower frequency, and vice versa, reflecting the constraint between the temporal and spatial domains.  

**4. Photon model**\\
The photon model focuses on the particle nature of light, and its basic unit of energy is called a photon.\\

Photons are massless particles that carry energy and momentum, described by the fundamental energy relation:
$$E = h\nu = \frac{hc}{\lambda}$$

where:\\
  * $h$: Planck constant,  
  * $\nu$: frequency of light,  
  * $c$: speed of light in vacuum,  
  * $\lambda$: wavelength of light.
Photon energy is directly proportional to frequency and inversely proportional to wavelength.

**4.1 Photoelectric Effect**\\
The photoelectric effect is key evidence for the photon model. An incident photon transfers its energy to an electron in a material. If the energy is sufficient to overcome atomic binding, the electron is emitted as a photoelectron.\\
{{ :en:yanding:imaging_basics:optics:geometric_optics:光9.png?400 |}}

**4.2 Photon Shot Noise**\\
Photon shot noise originates from the discrete nature of photons. It is particularly evident in low-light conditions, where the photon flux at the sensor is low.
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